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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 03 Nov 2009 08:51:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/03/t1257263695631vdfayiiajcly.htm/, Retrieved Wed, 01 May 2024 22:39:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=53198, Retrieved Wed, 01 May 2024 22:39:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-11-03 15:51:36] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
149.7	   
163.6	   
173.9	   
164.5	   
154.2	   
147.9	   
159.3	   
170.3	   
170	   
174.2	   
190.8	   
179.9	   
240.8	   
241.9	   
241.1	   
239.6	   
220.8	   
209.3	   
209.9	   
228.3	   
242.1	   
226.4	   
231.5	   
229.7	   
257.6	   
260	   
264.4	   
268.8	   
271.4	   
273.8	   
277.4	   
268.2	   
264.6	   
266.6	   
266	   
267.4	   
289.8	   
294	   
310.3	   
311.7	   
302.1	   
298.2	   
299.2	   
296.2	   
299	   
300	   
299.4	   
300.2	   
470.2	   
472.1	   
484.8	   
513.4	   
547.2	   
548.1	   
544.7	 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=53198&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=53198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=53198&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean275.39090909090913.936708371074819.7601113375146
Geometric Mean259.545475544324
Harmonic Mean246.186724356556
Quadratic Mean293.817412999669
Winsorized Mean ( 1 / 18 )275.40727272727313.925278676776819.7775052923407
Winsorized Mean ( 2 / 18 )275.4813.865574063404119.8679116162298
Winsorized Mean ( 3 / 18 )274.05090909090913.227215305277620.7187153732626
Winsorized Mean ( 4 / 18 )272.28363636363612.500402892803121.7819888445675
Winsorized Mean ( 5 / 18 )271.21090909090912.128269193131422.3618807244569
Winsorized Mean ( 6 / 18 )271.60363636363611.968580912040322.693052614985
Winsorized Mean ( 7 / 18 )251.4690909090916.8137980789563836.90586189892
Winsorized Mean ( 8 / 18 )251.7890909090916.6661594113722437.7712375853999
Winsorized Mean ( 9 / 18 )250.4963636363646.4468079767013738.8558748052761
Winsorized Mean ( 10 / 18 )251.1872727272736.1713245060161340.7023277551524
Winsorized Mean ( 11 / 18 )253.3272727272735.7107114515736544.3600197410545
Winsorized Mean ( 12 / 18 )257.2327272727274.9132727916897352.3546601580536
Winsorized Mean ( 13 / 18 )257.3272727272734.8801883929975352.7289629016178
Winsorized Mean ( 14 / 18 )260.0509090909094.3916371955596159.2150256295868
Winsorized Mean ( 15 / 18 )261.364.1086937473805863.6114580617319
Winsorized Mean ( 16 / 18 )261.3309090909093.9259148263497366.5656084377896
Winsorized Mean ( 17 / 18 )261.0836363636363.7474029288770169.6705535323568
Winsorized Mean ( 18 / 18 )260.2981818181823.4347741322327475.783201979857
Trimmed Mean ( 1 / 18 )272.65094339622613.277304922266820.5351119818733
Trimmed Mean ( 2 / 18 )269.67843137254912.444413602559721.6706419430707
Trimmed Mean ( 3 / 18 )266.42244897959211.395229363905123.3801743230810
Trimmed Mean ( 4 / 18 )263.44680851063810.370581591431225.4032819845238
Trimmed Mean ( 5 / 18 )260.7466666666679.3534996421422727.8769098885588
Trimmed Mean ( 6 / 18 )258.0697674418608.1168231944201231.7944300695461
Trimmed Mean ( 7 / 18 )258.0697674418606.3367617420392140.7258120073822
Trimmed Mean ( 8 / 18 )255.7641025641036.1163808364779941.8162487591894
Trimmed Mean ( 9 / 18 )256.5027027027035.8603434987396943.7692266260272
Trimmed Mean ( 10 / 18 )257.5514285714295.5650747221097646.2799587484764
Trimmed Mean ( 11 / 18 )258.6121212121215.2375931277895349.3761380279773
Trimmed Mean ( 12 / 18 )259.4645161290324.9333875652070752.5935805163408
Trimmed Mean ( 13 / 18 )259.8172413793104.7757213082349154.4037695271916
Trimmed Mean ( 14 / 18 )259.8172413793104.5405514616880257.2215167191871
Trimmed Mean ( 15 / 18 )260.2074074074074.3617722697698659.656348684416
Trimmed Mean ( 16 / 18 )260.0521739130434.1769453329952462.2589364191087
Trimmed Mean ( 17 / 18 )259.8428571428573.9377088541953165.988336559219
Trimmed Mean ( 18 / 18 )259.6315789473683.6015676625016772.08849125634
Median264.6
Midrange348
Midmean - Weighted Average at Xnp258.410714285714
Midmean - Weighted Average at X(n+1)p259.817241379310
Midmean - Empirical Distribution Function259.817241379310
Midmean - Empirical Distribution Function - Averaging259.817241379310
Midmean - Empirical Distribution Function - Interpolation260.207407407407
Midmean - Closest Observation258.410714285714
Midmean - True Basic - Statistics Graphics Toolkit259.817241379310
Midmean - MS Excel (old versions)259.817241379310
Number of observations55

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 275.390909090909 & 13.9367083710748 & 19.7601113375146 \tabularnewline
Geometric Mean & 259.545475544324 &  &  \tabularnewline
Harmonic Mean & 246.186724356556 &  &  \tabularnewline
Quadratic Mean & 293.817412999669 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 275.407272727273 & 13.9252786767768 & 19.7775052923407 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 275.48 & 13.8655740634041 & 19.8679116162298 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 274.050909090909 & 13.2272153052776 & 20.7187153732626 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 272.283636363636 & 12.5004028928031 & 21.7819888445675 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 271.210909090909 & 12.1282691931314 & 22.3618807244569 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 271.603636363636 & 11.9685809120403 & 22.693052614985 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 251.469090909091 & 6.81379807895638 & 36.90586189892 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 251.789090909091 & 6.66615941137224 & 37.7712375853999 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 250.496363636364 & 6.44680797670137 & 38.8558748052761 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 251.187272727273 & 6.17132450601613 & 40.7023277551524 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 253.327272727273 & 5.71071145157365 & 44.3600197410545 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 257.232727272727 & 4.91327279168973 & 52.3546601580536 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 257.327272727273 & 4.88018839299753 & 52.7289629016178 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 260.050909090909 & 4.39163719555961 & 59.2150256295868 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 261.36 & 4.10869374738058 & 63.6114580617319 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 261.330909090909 & 3.92591482634973 & 66.5656084377896 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 261.083636363636 & 3.74740292887701 & 69.6705535323568 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 260.298181818182 & 3.43477413223274 & 75.783201979857 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 272.650943396226 & 13.2773049222668 & 20.5351119818733 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 269.678431372549 & 12.4444136025597 & 21.6706419430707 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 266.422448979592 & 11.3952293639051 & 23.3801743230810 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 263.446808510638 & 10.3705815914312 & 25.4032819845238 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 260.746666666667 & 9.35349964214227 & 27.8769098885588 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 258.069767441860 & 8.11682319442012 & 31.7944300695461 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 258.069767441860 & 6.33676174203921 & 40.7258120073822 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 255.764102564103 & 6.11638083647799 & 41.8162487591894 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 256.502702702703 & 5.86034349873969 & 43.7692266260272 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 257.551428571429 & 5.56507472210976 & 46.2799587484764 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 258.612121212121 & 5.23759312778953 & 49.3761380279773 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 259.464516129032 & 4.93338756520707 & 52.5935805163408 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 259.817241379310 & 4.77572130823491 & 54.4037695271916 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 259.817241379310 & 4.54055146168802 & 57.2215167191871 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 260.207407407407 & 4.36177226976986 & 59.656348684416 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 260.052173913043 & 4.17694533299524 & 62.2589364191087 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 259.842857142857 & 3.93770885419531 & 65.988336559219 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 259.631578947368 & 3.60156766250167 & 72.08849125634 \tabularnewline
Median & 264.6 &  &  \tabularnewline
Midrange & 348 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 258.410714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 259.817241379310 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 259.817241379310 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 259.817241379310 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 260.207407407407 &  &  \tabularnewline
Midmean - Closest Observation & 258.410714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 259.817241379310 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 259.817241379310 &  &  \tabularnewline
Number of observations & 55 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=53198&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]275.390909090909[/C][C]13.9367083710748[/C][C]19.7601113375146[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]259.545475544324[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]246.186724356556[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]293.817412999669[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]275.407272727273[/C][C]13.9252786767768[/C][C]19.7775052923407[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]275.48[/C][C]13.8655740634041[/C][C]19.8679116162298[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]274.050909090909[/C][C]13.2272153052776[/C][C]20.7187153732626[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]272.283636363636[/C][C]12.5004028928031[/C][C]21.7819888445675[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]271.210909090909[/C][C]12.1282691931314[/C][C]22.3618807244569[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]271.603636363636[/C][C]11.9685809120403[/C][C]22.693052614985[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]251.469090909091[/C][C]6.81379807895638[/C][C]36.90586189892[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]251.789090909091[/C][C]6.66615941137224[/C][C]37.7712375853999[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]250.496363636364[/C][C]6.44680797670137[/C][C]38.8558748052761[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]251.187272727273[/C][C]6.17132450601613[/C][C]40.7023277551524[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]253.327272727273[/C][C]5.71071145157365[/C][C]44.3600197410545[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]257.232727272727[/C][C]4.91327279168973[/C][C]52.3546601580536[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]257.327272727273[/C][C]4.88018839299753[/C][C]52.7289629016178[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]260.050909090909[/C][C]4.39163719555961[/C][C]59.2150256295868[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]261.36[/C][C]4.10869374738058[/C][C]63.6114580617319[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]261.330909090909[/C][C]3.92591482634973[/C][C]66.5656084377896[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]261.083636363636[/C][C]3.74740292887701[/C][C]69.6705535323568[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]260.298181818182[/C][C]3.43477413223274[/C][C]75.783201979857[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]272.650943396226[/C][C]13.2773049222668[/C][C]20.5351119818733[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]269.678431372549[/C][C]12.4444136025597[/C][C]21.6706419430707[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]266.422448979592[/C][C]11.3952293639051[/C][C]23.3801743230810[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]263.446808510638[/C][C]10.3705815914312[/C][C]25.4032819845238[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]260.746666666667[/C][C]9.35349964214227[/C][C]27.8769098885588[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]258.069767441860[/C][C]8.11682319442012[/C][C]31.7944300695461[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]258.069767441860[/C][C]6.33676174203921[/C][C]40.7258120073822[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]255.764102564103[/C][C]6.11638083647799[/C][C]41.8162487591894[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]256.502702702703[/C][C]5.86034349873969[/C][C]43.7692266260272[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]257.551428571429[/C][C]5.56507472210976[/C][C]46.2799587484764[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]258.612121212121[/C][C]5.23759312778953[/C][C]49.3761380279773[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]259.464516129032[/C][C]4.93338756520707[/C][C]52.5935805163408[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]259.817241379310[/C][C]4.77572130823491[/C][C]54.4037695271916[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]259.817241379310[/C][C]4.54055146168802[/C][C]57.2215167191871[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]260.207407407407[/C][C]4.36177226976986[/C][C]59.656348684416[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]260.052173913043[/C][C]4.17694533299524[/C][C]62.2589364191087[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]259.842857142857[/C][C]3.93770885419531[/C][C]65.988336559219[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]259.631578947368[/C][C]3.60156766250167[/C][C]72.08849125634[/C][/ROW]
[ROW][C]Median[/C][C]264.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]348[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]258.410714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]259.817241379310[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]259.817241379310[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]259.817241379310[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]260.207407407407[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]258.410714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]259.817241379310[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]259.817241379310[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]55[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=53198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=53198&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean275.39090909090913.936708371074819.7601113375146
Geometric Mean259.545475544324
Harmonic Mean246.186724356556
Quadratic Mean293.817412999669
Winsorized Mean ( 1 / 18 )275.40727272727313.925278676776819.7775052923407
Winsorized Mean ( 2 / 18 )275.4813.865574063404119.8679116162298
Winsorized Mean ( 3 / 18 )274.05090909090913.227215305277620.7187153732626
Winsorized Mean ( 4 / 18 )272.28363636363612.500402892803121.7819888445675
Winsorized Mean ( 5 / 18 )271.21090909090912.128269193131422.3618807244569
Winsorized Mean ( 6 / 18 )271.60363636363611.968580912040322.693052614985
Winsorized Mean ( 7 / 18 )251.4690909090916.8137980789563836.90586189892
Winsorized Mean ( 8 / 18 )251.7890909090916.6661594113722437.7712375853999
Winsorized Mean ( 9 / 18 )250.4963636363646.4468079767013738.8558748052761
Winsorized Mean ( 10 / 18 )251.1872727272736.1713245060161340.7023277551524
Winsorized Mean ( 11 / 18 )253.3272727272735.7107114515736544.3600197410545
Winsorized Mean ( 12 / 18 )257.2327272727274.9132727916897352.3546601580536
Winsorized Mean ( 13 / 18 )257.3272727272734.8801883929975352.7289629016178
Winsorized Mean ( 14 / 18 )260.0509090909094.3916371955596159.2150256295868
Winsorized Mean ( 15 / 18 )261.364.1086937473805863.6114580617319
Winsorized Mean ( 16 / 18 )261.3309090909093.9259148263497366.5656084377896
Winsorized Mean ( 17 / 18 )261.0836363636363.7474029288770169.6705535323568
Winsorized Mean ( 18 / 18 )260.2981818181823.4347741322327475.783201979857
Trimmed Mean ( 1 / 18 )272.65094339622613.277304922266820.5351119818733
Trimmed Mean ( 2 / 18 )269.67843137254912.444413602559721.6706419430707
Trimmed Mean ( 3 / 18 )266.42244897959211.395229363905123.3801743230810
Trimmed Mean ( 4 / 18 )263.44680851063810.370581591431225.4032819845238
Trimmed Mean ( 5 / 18 )260.7466666666679.3534996421422727.8769098885588
Trimmed Mean ( 6 / 18 )258.0697674418608.1168231944201231.7944300695461
Trimmed Mean ( 7 / 18 )258.0697674418606.3367617420392140.7258120073822
Trimmed Mean ( 8 / 18 )255.7641025641036.1163808364779941.8162487591894
Trimmed Mean ( 9 / 18 )256.5027027027035.8603434987396943.7692266260272
Trimmed Mean ( 10 / 18 )257.5514285714295.5650747221097646.2799587484764
Trimmed Mean ( 11 / 18 )258.6121212121215.2375931277895349.3761380279773
Trimmed Mean ( 12 / 18 )259.4645161290324.9333875652070752.5935805163408
Trimmed Mean ( 13 / 18 )259.8172413793104.7757213082349154.4037695271916
Trimmed Mean ( 14 / 18 )259.8172413793104.5405514616880257.2215167191871
Trimmed Mean ( 15 / 18 )260.2074074074074.3617722697698659.656348684416
Trimmed Mean ( 16 / 18 )260.0521739130434.1769453329952462.2589364191087
Trimmed Mean ( 17 / 18 )259.8428571428573.9377088541953165.988336559219
Trimmed Mean ( 18 / 18 )259.6315789473683.6015676625016772.08849125634
Median264.6
Midrange348
Midmean - Weighted Average at Xnp258.410714285714
Midmean - Weighted Average at X(n+1)p259.817241379310
Midmean - Empirical Distribution Function259.817241379310
Midmean - Empirical Distribution Function - Averaging259.817241379310
Midmean - Empirical Distribution Function - Interpolation260.207407407407
Midmean - Closest Observation258.410714285714
Midmean - True Basic - Statistics Graphics Toolkit259.817241379310
Midmean - MS Excel (old versions)259.817241379310
Number of observations55



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')